Artificial Intelligence #45: The significance of Probabilistic Graphical Models

Welcome to Artificial Intelligence #45

?Firstly, before we proceed, let us pray for Ukraine

Let us hope that more innocent lives are not lost in Ukraine.

In this edition, we look at Probabilistic Graphical Models. We (Dr?Amita Kapoor and I) are implementing similar ideas at Digitty. If you are a media agency and want to work on an early adopter program with us, please let me know. It could be a chance to develop custom algorithms to understand project risk especially at early stages of fast moving digital project where you need to understand risk

?Background

Every year, when I develop my course at the #universityofoxford, I make a presentation for topics we should expand – and this year, we expanded a lot on Bayesian specifically PGMs (probabilistic graphical models). In a nutshell, A graphical model or probabilistic graphical model (PGM) or structured probabilistic model is a probabilistic model for which a graph expresses the conditional dependence structure between random variables.

?The best known book on this subject is By Daphne Koller and Nir Friedman – a massive yet readable book which I recommend (there is a version on the web as well). This post is based on ideas from the book

?Probabilistic Graphical models

First, we construct a declarative model of the system about which we would model like to reason. On this, we build a reasoning algorithm. ?Models for complex systems involve considerable uncertainty. ?We can model this uncertainty using probability theory.?Using the calculus of probability theory, we can model multiple possible outcomes and their likelihood. Multiple interrelated aspects which affect the outcome can be modelled as a reasoning task ?with each domain characterized as a set of random variables. When we do so, we can reason probabilistically about the values of one or more of the variables, possibly given observations about some others. To do this, we need to construct joint probability distributions for the variables. ?

?Probabilistic graphical models use a graph-based representation as the basis for compactly encoding a complex distribution over a high-dimensional space. Here, the nodes correspond to the variables and the edges correspond to direct probabilistic interactions between them. There are two families of graphical representations: Bayesian networks which uses a directed graph (where the edges have a source and a target) and Markov networks which use an undirected graph.

The graphical language exploits the structure that is seen in many distributions i.e. the property that variables tend to interact directly only with very few others.

?Advantages

There are a number of advantages to this approach

a)?????The model could be more explainable

b)????You can use the model for reasoning by a human expert or automatically

c)????You can incorporate expert knowledge)

d)????The model can sometimes reveal surprising connections between variables and provide novel insights about a domain.

e)????You can potentially build causal models which are lacking in the current machine learning structure because the PGM gives you a set of relationships in the form of X causes Y

f)?????You could build counterfactual models based on interventions i.e. understand the impact of intervention ex if a variable were to be changed by x percent, would the outcome change? i.e. what-if reasoning

I hope you found this analysis useful in understanding the power of PGMs - especially in the ability to potentially construct explainable, causal and counterfactual models. In the next newsletter also I will explore this subject in more detail. If you are a media agency and are interested in working with such models for understanding project risk, please contact me?